Maybe you could recognize there are some winning ideas here and try to exploit them instead of accepting a draw-your opponent may also make mistakes after all. But i doubt you could found out that 1.Kd1 is the only winning move(as Houdini said after 30s)
The last part of your statement is why I take a draw most likely.
You wouldnt know the last part of my statment if position appeared before you during the game. What you might know is that you cant loose here(unless you play very bad or you loose on time) and that you have reasonable winning chances. If you realise that you shoudnt take draw unless you have less than 1 min time left. But even to get this it takes some time, depending on your strength.
Computer cant give you a plan, but it can help you to construct your plan a lot. At least it shows you which plan is right and which is wrong.
EIther way, I still take a draw. If you realized that I tend to get a bit confused when I start having to calculate a bunch of what ifs, maybe then you'd understand. If you considered that the line of best moves, that has many possible variations is 30 moves to win, you'll understand why I am not going to risk losing, unless you are better rated and/or in a tourney against me.
If you are lower rated, I won't waste my time. The problem I find with postions like this is,if you just start winging it, though things seem ok and you may have widdled down the final list of moves to 15, thinking your worst outcome is a draw, you very well might have missed something and it could be a sure loss, that you can't see.